# Hans Joachim HauboldUnited Nations Organization · Office for Outer Space Affairs

Hans Joachim Haubold

Prof. Dr.

## About

419

Publications

74,546

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

11,690

Citations

Citations since 2017

Introduction

Research topic: 'Fractional quantum diffusion (walk) and neutrino entanglement entropy for the interpretation of solar neutrino diffusion entropy analysis.'
SUMMARY EXPOSITION AVAILABLE AT
https://www.amazon.com/author/hansjhaubold
AND
https://www.growkudos.com/projects/a-m-mathai-centre-for-mathematical-and-statistical-sciences-nurturing-the-love-for-mathematics

Additional affiliations

January 1996 - December 2012

January 1989 - December 2011

**Independent Researcher**

November 1988 - present

## Publications

Publications (419)

A Course for Physicists and Engineers In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements such as theorems and proofs too much. It is also designed to...

A Course for Physicists and Engineers This textbook offers an introduction to concepts of probability theory, probability distributions relevant in the applied sciences, as well as basics of sampling distributions, estimation and hypothesis testing. As the basis for courses on space and atmospheric science, remote sensing, geographic information sy...

This is a modified version of Module 10 of the Centre for Mathematical and Statistical Sciences (CMSS). CMSS modules are notes prepared on various topics with many examples from real-life situations and exercises so that the subject matter becomes interesting to students. These modules are used for undergraduate level courses and graduate level tra...

Broadens understanding of research fields through the framework of fractional and multivariate calculus ▶ Reinforces basic principles of fractional calculus ▶ Maximizes readers insight into mathematical models and applications This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization prob...

Fractional calculus in terms of mathematics and statistics and its applications to problems in natural sciences is NOT yet part of university teaching curricula. This book is one attempt to provide an approach to include topics of fractional calculus into university curricula. Additionally the material is useful for people who do research work in t...

The original version of the book was inadvertently published with incorrect abstract. This has now been amended in the chapters.

This Special Issue of the journal Axioms collates submissions in which the authors report their perceptions and results in the field of mathematical physics and/or physical mathematics without any preconditions of the specific research topic [...]

Several generalizations or extensions of the Boltzmann–Gibbs thermostatistics, based on non-standard entropies, have been the focus of considerable research activity in recent years. Among these, the power-law, non-additive entropies Sq≡k1−∑ipiqq−1(q∈R;S1=SBG≡−k∑ipilnpi) have harvested the largest number of successful applications. The specific str...

We will keep utilizing the same notations in this chapter. More specifically, lower-case letters x, y, … will denote real scalar variables, whether mathematical or random. Capital letters X, Y, … will be used to denote real matrix-variate mathematical or random variables, whether square or rectangular matrices are involved. A tilde will be placed a...

The requisite theory for the study of Principal Component Analysis has already been introduced in Chap. 1 , namely, the problem of optimizing a real quadratic form that is subject to a constraint. We formulate the problem with respect to a practical situation consisting of selecting the most ``relevant'' variables in a study. Principal component an...

This chapter relies on various results presented in Chap. 1 . We introduce a class of integrals called the real matrix-variate Gaussian integrals and complex matrix-variate Gaussian integrals wherefrom a statistical density referred to as the matrix-variate Gaussian density and, as a special case, the multivariate Gaussian or normal density will be...

Thus far, we have primarily been dealing with distributions involving real positive definite or Hermitian positive definite matrices. We have already considered rectangular matrices in the matrix-variate Gaussian case.

We will employ the same notations as in the previous chapters. Lower-case letters x, y, … will denote real scalar variables, whether mathematical or random. Capital letters X, Y, … will be used to denote real matrix-variate mathematical or random variables, whether square or rectangular matrices are involved. A tilde will be placed on top of letter...

It is assumed that the reader has had adequate exposure to basic concepts in Probability, Statistics, Calculus and Linear Algebra. This chapter provides a brief review of the results that will be needed in the remainder of this book. No detailed discussion of these topics will be attempted. For essential materials in these areas, the reader is, for...

We will utilize the same notations as in the previous chapters. Lower-case letters x , y , … will denote real scalar variables, whether mathematical or random. Capital letters X , Y , … will be used to denote real matrix-variate mathematical or random variables, whether square or rectangular matrices are involved. A tilde will be placed on top of l...

We will utilize the same notations as in the previous chapters. Lower-case letters x , y , … will denote real scalar variables, whether mathematical or random. Capital letters X , Y , … will be used to denote real matrix-variate mathematical or random variables, whether square or rectangular matrices are involved. A tilde will be placed on top of l...

We will utilize the same notations as in the previous chapters. Lower-case letters x , y , … will denote real scalar variables, whether mathematical or random. Capital letters X , Y , … will be used to denote real matrix-variate mathematical or random variables, whether square or rectangular matrices are involved. A tilde will be placed on top of l...

We will use the same notations as in the previous chapters. Lower-case letters x , y , … will denote real scalar variables, whether mathematical or random. Capital letters X , Y , … will be used to denote real matrix-variate mathematical or random variables, whether square or rectangular matrices are involved.

It is assumed that the reader has had adequate exposure to basic concepts in Probability, Statistics, Calculus and Linear Algebra. This chapter will serve as a review of the basic ideas about the univariate Gaussian, or normal, distribution as well as related distributions. We will begin with a discussion of the univariate Gaussian density.

It is assumed that the readers are familiar with the concept of testing statistical hypotheses on the parameters of a real scalar normal distribution or independent real scalar normal distributions. The likelihood ratio criterion is employed for testing various hypotheses on the parameters of one or more real multivariate Gaussian (or normal) distr...

The notations introduced in the preceding chapters will still be followed in this one. Lower-case letters such as x , y will be utilized to represent real scalar variables, whether mathematical or random. Capital letters such as X , Y will be used to denote vector/matrix random or mathematical variables. A tilde placed on top of a letter will indic...

Real scalar mathematical as well as random variables will be denoted by lower-case letters such as x, y, z, and vector/matrix variables, whether mathematical or random, will be denoted by capital letters such as X, Y, Z, in the real case. Complex variables will be denoted with a tilde: \(\tilde {x},\tilde {y}, \tilde {X},\tilde {Y}, \) for instance...

We will employ the same notations as in the previous chapters. Lower-case letters x, y, … will denote real scalar variables, whether mathematical or random. Capital letters X, Y, … will be used to denote real matrix-variate mathematical or random variables, whether square or rectangular matrices are involved. A tilde will be placed on top of letter...

Forty years of research topic 'Education, Teaching, Research in Space Science' briefly summarized.

This paper reviews briefly the history of the Michelson experiment, invented and performed for the first time in the Astrophysical Observatory Potsdam in 1881. The paper draws attention to the International Michelson Colloquium, held from April 27 to April 30, 1981 in Potsdam (Germany). This paper is an attempt to reconsider a scientific event orga...

Forty years of research topic 'Solar Neutrino Data Analysis' briefly summarized.

Forty years of research topic 'Michelson Livingston' briefly summarized.

This paper reviews in detail the history of the Michelson experiment, invented and performed for the first time in the Astrophysical Observatory Potsdam in 1881. All documents still available in German archives concerning Michelson’s travel to Berlin and Potsdam are discussed. The paper draws attention to the International Michelson Colloquium, hel...

This paper reviews briefly the history of the Michelson experiment, invented and performed for the first time in the Astrophysical Observatory Potsdam in 1881. The paper draws attention to the International Michelson Colloquium, held from April 27 to April 30, 1981, published by Astronomische Nachrichten and by the American Institute of Physics.

In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, mult...

The closed forms of the non-resonant thermonuclear function in the Maxwell–Boltzmann and Tsallis case with depleted tail are obtained in generalized special functions. The results are written in terms of H-function of two variables. The importance of the results in this paper lies in the fact that the reaction rate probability integrals in Maxwell-...

A status report for an attempt to implement a project of education, teaching, and research in space science and technology in the spirit of the United Nations is briefly summarized in this Viewpoint.

A real scalar variable integral is known in the literature by different names in different disciplines. It is basically a Bessel integral called specifically Krätzel integral. An integral transform with this Krätzel function as kernel is known as Krätzel transform. This article examines some mathematical properties of Krätzel integral, its connecti...

A brief history of the Centre for Mathematical and Statistical Sciences, Kerala, India, is given and an overview of Mathai's research and education programs in the following topics is outlined: Fractional Calculus; Functions of Matrix Argument - M-transforms, M-convolutions; Kraetzel integrals; Pathway Models; Geometrical Probabilities; Astrophysic...

This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, and gamma families of distri...

Based on resolutions of the United Nations General Assembly, UN-affiliated Regional Centres for Space Science and Technology Education were established in China, India, Morocco, Nigeria, Brazil/Mexico, and Jordan. Simultaneously, education curricula at the university level were developed for the core disciplines of remote sensing, satellite communi...

General notations on matrices, determinants, traces etc. are given in the introduction to Chap. 2 and hence they will not be repeated here. Before starting the discussion, we will need some Jacobians of matrix transformations here. For results on Jacobians, see Mathai [3]. For the real matrix-variate case, the determinant of X will be denoted by ei...

All the matrices appearing in this chapter are p × p real positive definite unless stated otherwise. In order to avoid too many symbols we will use \(u_1=\frac {x_2}{x_1}\) for the ratio of x2 to x1 in the real scalar variable case, \(U_1=X_2^{\frac {1}{2}}X_1^{-1}X_2^{\frac {1}{2}}\), symmetric ratio, in the real p × p matrix-variate case. The cor...

This monograph will examine a new definition for fractional integrals in terms of the distributions of products and ratios of statistically independently distributed positive scalar random variables or in terms of Mellin convolutions of products and ratios in the case of real scalar variables. The idea will be generalized to cover real multivariate...

The laws of nature are fundamentally random. This Springer Briefs in Mathematical Physics is an attempt to illustrate elements of a research programme in mathematics and statistics applied to selected problems in physics, particularly the relations between solar neutrinos, diffusion, entropy, and fractional calculus as they appear in neutrino astro...

In Chaps. 2, 3, 4, and 5 we considered the real scalar variable case, real multivariate case, real one matrix-variate case, real several matrix-variate case. In the present chapter we will look into fractional calculus in the complex domain. Since we will be dealing with p × p Hermitian positive definite matrices, for p = 1 Hermitian positive defin...

When going from a one-variable function to many-variable function there is no unique one to one correspondence. Many types of multivariate functions can be considered when one has the preselected one-variable function. Hence there is nothing called the multivariate analogue of a univariate operator or univariate integral. Hence we construct one mul...

Based on the results of the diffusion entropy analysis of Super-Kamiokande solar neutrino data, a generalized entropy, introduced earlier by the first author is optimized under various conditions and it is shown that Maxwell–Boltzmann distribution, Raleigh distribution and other distributions can be obtained through such optimization procedures. So...

OSO absorption spectra may offer a clue to the distribution of intervening matter clouds at z = 0 … 3. We tackle 1) the question of the occurrence of metal absorption lines of different ionisation levels in the same redshift systems by investigating the radiation transport through an inhomogeneous temperature profile; 2) the clustering properties o...

Talcing into account vacuum polarization effects and a coherent massive scalar field we consider a singularity free cosmological model from which an intermediate inflationary stage follows quite naturally. According to the ideas of Tryon, Fomin, Zeldovich and others on the spontaneous creation of an universe by a quantum process the newly created u...

We consider two density perturbation modes with significantly different length scales λ and L (λ ≪ L) in a homogeneous Universe within Newtonian approximation. For the two modes the coupling terms in the corresponding Euler-Lagrange and Poisson equations are taken into account within lowest order of approximation. We assume that the λ - nods (high-...

The general linear model, discussed in Chapter 4, will be re-examined here in order to bring out some more interesting points and to talk about estimability of linear functions of the parameters, Gauss–Markov setup, and related matters.

In recent decades, the field of fractional calculus has attracted interest of researchers in several areas including mathematics, physics, chemistry, engineering, and even finance and social sciences.

A vector is a quantity that is determined by both its magnitude and its direction: thus, it is a directed line segment.

There are various types of models that one can construct for a given set of data. The types of model that is chosen depends upon the type of data for which the model is to be constructed. If the data are coming from a deterministic situation, then there may be already an underlying mathematical formula such as a physical law.

Here, we look at model building in general. First, we will deal with real scalar variable cases. Then generalized models, matrix-variate cases, etc., will be examined. First, let us look at the effect of power transformations and exponentiations on a given model. This will give some ideas about the changes required in a given situation of building...

We considered models which were governed by definite mathematical rules or fully deterministic in nature. There was no chance variation involved. But most of the practical situations, mostly in social sciences, economics, commerce, management, etc., as well as many physical phenomena, are non-deterministic in nature. Earthquake at a place cannot be...

Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional...

This paper contains an overview and summary on the achievements of the United
Nations basic space science initiative in terms of donated and provided
planetariums, astronomical telescopes, and space weather instruments,
particularly operating in developing nations. This scientific equipment has
been made available to respective host countries, part...

A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill
University, Canada, and Director of the Centre for Mathematical and Statistical
Sciences, India. He has published over 300 research papers and more than 25
books on topics in mathematics, statistics, physics, astrophysics, chemistry,
and biology. He is a Fellow of the Institu...

This paper is in continuation of the authors' recently published paper
(Journal of Mathematical Physics 55(2014)083519) in which computational
solutions of an uni?ed reaction-diffusion equation of distributed order
associated with Caputo derivatives as the time-derivative and Riesz-Feller
derivative as space derivative is derived. In the present pa...

We are triply lucky. A thoughtful and sensitive monograph has been thoughtfully and sensitively translated from Japanese (2010) to English (2014); and the solar neutrino problem appears with a human touch. Sakurai’s book contains some questions and some technical expositions concerning the evolution and internal structure of the Sun. He explains wi...

An entropy for the scalar variable case, parallel to Havrda-Charvat entropy
was introduced by the first author and the properties and its connection to
Tsallis non-extensive statistical mechanics and the Mathai pathway model were
examined by the authors in previous papers. In the current paper we extend the
entropy to cover scalar case, multivariab...

It has been 20 years since planning began for the 1995 United Nations
International Conference on Near-Earth Objects. The conference proceedings
established the scientific basis for an international organizational framework
to support research and collective actions to mitigate a potential near-Earth
object (NEO) threat to the planet. Since that ti...

After collecting data from observations or experiments, the next step is to
build an appropriate mathematical or stochastic model to describe the data so
that further studies can be done with the help of the models. In this article,
the input-output type mechanism is considered first, where reaction, diffusion,
reaction-diffusion, and production-de...

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by th...

Natural history, interpreted through the geological and
paleontological records, has taught us that impacts of near-Earth
objects (NEOs) pose a serious threat to humankind. Astronomy tells
us that it is practically inevitable that Earth will be struck by a globally
or regionally civilization threatening NEO in the future. The good news
is that give...

In 1910 Einstein published a crucial aspect of his understanding of Boltzmann
entropy. He essentially argued that the likelihood function of any system
composed by two probabilistically independent subsystems {\it ought} to be
factorizable into the likelihood functions of each of the subsystems.
Consistently he was satisfied by the fact that Boltzm...

Possible modification in the velocity distribution in the non-resonant
reaction rates leads to an extended reaction rate probability integral. The
closed form representation for these thermonuclear functions are used to obtain
the stellar luminosity and neutrino emission rates. The composite parameter {C}
that determines the standard nuclear reacti...

We are going back to the roots of the original solar neutrino problem: the analysis of data from solar neutrino experiments. The application of standard deviation analysis (SDA) and diffusion entropy analysis (DEA) to the Super-Kamiokande I and II data reveals that they represent a non-Gaussian signal. The Hurst exponent is different from the scali...

This article is in continuation of the authors research attempts to derive computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as space derivative. This article presents computational solutions of distributed order fractional rea...

Globally there is growing interest in better understanding solar-terrestrial interactions, particularly patterns and trends in space weather. This is not only for scientific reasons, but also because the reliable operation of ground-based and space-based assets and infrastructures is increasingly dependent on their robustness against the detrimenta...

C46 is a Commission of the Executive Committee of the IAU under Division XII Union-Wide Activities. Aiming at improvement of astronomy education and research at all levels worldwide (through the various projects it initiates),maintains, develops, as well as through the dissemination of information. C46 has 332 members and it was managed by the Orga...

Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in various problems of mathematics, statistics and natural sciences. In this survey we start with considering the case of a Gauss hypergeometric function with the argument being a rectangular matrix. Subsequently, some fractional integral operat...

In this article we examine the densities of a product and a ratio of two
real positive scalar random variables $x_1$ and $x_2$, which are
statistically independently distributed, and we consider the density of
the product $u_1=x_1x_2$ as well as the density of the ratio
$u_2={{x_2}\over{x_1}}$ and show that Kober operator of the second kind
is avai...

In this article we examine the densities of a product and a ratio of two
real positive definite matrix-variate random variables $X_1$ and $X_2$,
which are statistically independently distributed, and we consider the
density of the product $U_1=X_2^{1\over2}X_1X_2^{1\over2}$ as well as
the density of the ratio $U_2=X_2^{1\over2}X_1^{-1}X_2^{1\over2}...

In this article we define Kober fractional integral operators in the
multivariable case. First we consider one sequence of independent random
variables and an arbitrary function, which can act as the joint density
of another sequence of random variables. Then we define a concept,
analogous to the concept of Kober operators in the scalar variable ca...

In the preceding articles we considered fractional integral transforms
involving one real scalar variable, one real matrix variable and real
scalar multivariable case. In the present paper we consider the
multivariable case when the arbitrary function is a real-valued scalar
function of many $p\times p$ real matrix variables $X_1,...,X_k$.
Extensio...

The pathway idea is a way of going from one family of functions to
another family of functions and yet another family of functions through
a parameter in the model so that a switching mechanism is introduced
into the model through a parameter. The advantage of the idea is that
the model can cover the ideal or stable situation in a physical
situatio...

Based on resolutions of the United Nations General Assembly, Regional Centres for Space Science and Technology Education were established in India, Morocco, Nigeria, Brazil/Mexico, and Jordan. Simultaneously, education curricula were developed for the core disciplines of remote sensing, satellite communications, satellite meteorology, space and atm...

The Silences of the Archives, the Reknown of the Story.
The Martin Guerre affair has been told many times since Jean de Coras and Guillaume Lesueur published their stories in 1561. It is in many ways a perfect intrigue with uncanny resemblance, persuasive deception and a surprizing end when the two Martin stood face to face, memory to memory, befor...

The United Nations Human Space Technology Initiative (HSTI) aims at promoting
international cooperation in human spaceflight and space exploration-related
activities; creating awareness among countries on the benefits of utilizing
human space technology and its applications; and building capacity in
microgravity education and research. HSTI has bee...

In 2010, the Human Space Technology Initiative (HSTI) was launched by the
United Nations Office for Outer Space Affairs (UNOOSA) within the United
Nations Programme on Space Applications. The Initiative aims at promoting
international cooperation in human spaceflight and space exploration-related
activities, creating awareness among countries on th...

This paper deals with the investigation of the computational solutions of an
unified fractional reaction-diffusion equation, which is obtained from the
standard diffusion equation by replacing the time derivative of first order by
the generalized fractional time-derivative defined by Hilfer (2000), the space
derivative of second order by the Riesz-...

This article is in continuation of our earlier article [37] in which
computational solution of an unified reaction-diffusion equation of distributed
order associated with Caputo derivatives as the time-derivative and
Riesz-Feller derivative as space derivative is derived. In this article, we
present computational solutions of distributed order frac...